Question

The domain of the function, f(x) = $\sqrt{x-1}+\sqrt{5-x}$ is

• A. $[1,\infty )$
• B. $(\infty ,5)$
• C. (1, 5)
• D. [1, 5]

Answer 1

The correct option is D [1, 5]

Given,

$f\left(x\right)=\sqrt{x-1}+\sqrt{5-x}$

For given function to be defined,
$x-1\ge 0$ and $5-x\ge 0$
$\Rightarrow x\ge 1$ and $x\le 5$

$\therefore x\in [1,5]$